TSTP Solution File: GEO221+2 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO221+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 23:22:30 EDT 2023
% Result : Theorem 9.22s 2.05s
% Output : Proof 13.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO221+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 23:49:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.48/1.06 Prover 4: Preprocessing ...
% 2.48/1.07 Prover 1: Preprocessing ...
% 2.87/1.11 Prover 2: Preprocessing ...
% 2.87/1.11 Prover 0: Preprocessing ...
% 2.87/1.11 Prover 3: Preprocessing ...
% 2.87/1.11 Prover 6: Preprocessing ...
% 2.87/1.11 Prover 5: Preprocessing ...
% 4.52/1.37 Prover 5: Proving ...
% 5.04/1.40 Prover 2: Proving ...
% 5.04/1.45 Prover 3: Constructing countermodel ...
% 5.04/1.45 Prover 6: Constructing countermodel ...
% 5.04/1.46 Prover 1: Constructing countermodel ...
% 5.04/1.59 Prover 6: gave up
% 5.04/1.59 Prover 4: Constructing countermodel ...
% 5.04/1.59 Prover 3: gave up
% 5.04/1.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.04/1.61 Prover 1: gave up
% 5.04/1.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.04/1.61 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 6.10/1.66 Prover 8: Preprocessing ...
% 6.10/1.66 Prover 7: Preprocessing ...
% 7.01/1.67 Prover 9: Preprocessing ...
% 7.01/1.68 Prover 0: Proving ...
% 7.25/1.70 Prover 7: Warning: ignoring some quantifiers
% 7.25/1.71 Prover 7: Constructing countermodel ...
% 7.46/1.78 Prover 8: Warning: ignoring some quantifiers
% 7.46/1.78 Prover 8: Constructing countermodel ...
% 8.16/1.86 Prover 8: gave up
% 8.67/1.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.67/1.95 Prover 10: Preprocessing ...
% 9.22/1.97 Prover 7: gave up
% 9.22/1.97 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.22/1.99 Prover 10: Warning: ignoring some quantifiers
% 9.22/1.99 Prover 11: Preprocessing ...
% 9.22/2.00 Prover 9: Constructing countermodel ...
% 9.22/2.00 Prover 10: Constructing countermodel ...
% 9.22/2.05 Prover 0: proved (1413ms)
% 9.22/2.05
% 9.22/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.22/2.05
% 9.22/2.05 Prover 9: stopped
% 9.22/2.07 Prover 5: stopped
% 9.22/2.07 Prover 2: stopped
% 9.22/2.07 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.22/2.07 Prover 10: gave up
% 9.22/2.07 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.22/2.07 Prover 13: Preprocessing ...
% 9.22/2.07 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 9.96/2.09 Prover 19: Preprocessing ...
% 9.96/2.09 Prover 16: Preprocessing ...
% 10.16/2.12 Prover 16: Warning: ignoring some quantifiers
% 10.38/2.13 Prover 16: Constructing countermodel ...
% 10.38/2.14 Prover 13: Warning: ignoring some quantifiers
% 10.38/2.15 Prover 13: Constructing countermodel ...
% 10.38/2.16 Prover 11: Constructing countermodel ...
% 10.38/2.17 Prover 19: Warning: ignoring some quantifiers
% 10.38/2.18 Prover 19: Constructing countermodel ...
% 11.12/2.25 Prover 13: gave up
% 11.12/2.27 Prover 19: gave up
% 11.12/2.28 Prover 16: gave up
% 11.87/2.45 Prover 4: Found proof (size 119)
% 11.87/2.45 Prover 4: proved (1810ms)
% 11.87/2.45 Prover 11: stopped
% 11.87/2.45
% 11.87/2.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.87/2.45
% 11.87/2.47 % SZS output start Proof for theBenchmark
% 11.87/2.47 Assumptions after simplification:
% 11.87/2.47 ---------------------------------
% 11.87/2.47
% 11.87/2.47 (con)
% 11.87/2.50 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5:
% 11.87/2.50 $i] : ( ~ (v4 = 0) & orthogonal_through_point(v2, v1) = v5 &
% 11.87/2.50 orthogonal_through_point(v2, v0) = v3 & apart_point_and_line(v1, v3) = v4 &
% 11.87/2.50 distinct_lines(v3, v5) = 0 & $i(v5) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.87/2.50
% 11.87/2.50 (cu1)
% 12.71/2.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 12.71/2.51 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 12.71/2.51 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 12.71/2.51 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 12.71/2.51 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0,
% 12.71/2.51 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 12.71/2.51 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 12.71/2.51 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) =
% 12.71/2.51 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3)
% 12.71/2.51 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 12.71/2.51 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 &
% 12.71/2.51 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6
% 12.71/2.51 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 12.71/2.51 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 12.71/2.51 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4)
% 12.71/2.51 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 12.71/2.51 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 12.71/2.51 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 12.71/2.51 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 =
% 12.71/2.51 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 12.71/2.51 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) =
% 12.71/2.51 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 12.71/2.51 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9:
% 12.71/2.51 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) =
% 12.71/2.51 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7
% 12.71/2.51 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 12.71/2.51 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 12.71/2.51 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4)
% 12.71/2.51 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 12.71/2.51 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 12.71/2.51 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 &
% 12.71/2.51 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0:
% 12.71/2.51 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 12.71/2.51 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~
% 12.71/2.51 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 12.71/2.51 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 12.71/2.52 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1,
% 12.71/2.52 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 12.71/2.52 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 12.71/2.52 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3)
% 12.71/2.52 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 12.71/2.52 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 12.71/2.52 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 12.71/2.52 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 12.71/2.52
% 12.71/2.52 (cup1)
% 12.71/2.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 12.71/2.52 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~
% 12.71/2.52 (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 12.71/2.52 [v5: any] : ? [v6: any] : (convergent_lines(v1, v2) = v6 &
% 12.71/2.52 distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : !
% 12.71/2.52 [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~
% 12.71/2.52 (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) |
% 12.71/2.52 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 12.71/2.52 (apart_point_and_line(v0, v1) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 =
% 12.71/2.52 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 12.71/2.52 int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) =
% 12.71/2.52 v3) | ~ (convergent_lines(v1, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 12.71/2.52 $i(v0) | ? [v5: any] : ? [v6: any] : (apart_point_and_line(v0, v2) = v6 &
% 12.71/2.52 distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : !
% 12.71/2.52 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0,
% 12.71/2.52 v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 12.71/2.52 $i(v0) | ? [v4: any] : ? [v5: any] : (apart_point_and_line(v0, v1) = v4 &
% 12.71/2.52 convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) & ! [v0: $i] : !
% 12.71/2.52 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0,
% 12.71/2.52 v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 12.71/2.52 $i(v0) | ? [v4: any] : ? [v5: any] : (apart_point_and_line(v0, v2) = v4 &
% 12.71/2.52 convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0)))
% 12.71/2.52
% 12.71/2.52 (oac1)
% 12.71/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 12.71/2.53 (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) |
% 12.71/2.53 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7:
% 12.71/2.53 any] : ? [v8: any] : (unorthogonal_lines(v0, v1) = v6 &
% 12.71/2.53 convergent_lines(v1, v2) = v8 & convergent_lines(v0, v2) = v7 &
% 12.71/2.53 convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4
% 12.71/2.53 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 12.71/2.53 : ! [v3: any] : ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~
% 12.71/2.53 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 12.71/2.53 [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 12.71/2.53 (unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 &
% 12.71/2.53 convergent_lines(v1, v2) = v8 & convergent_lines(v0, v1) = v5 & ( ~ (v6 =
% 12.71/2.53 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0:
% 12.71/2.53 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 12.71/2.53 (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ~
% 12.71/2.53 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any]
% 12.71/2.53 : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0,
% 12.71/2.53 v1) = v6 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5
% 12.71/2.53 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) &
% 12.71/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 12.71/2.53 (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ~
% 12.71/2.53 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any]
% 12.71/2.53 : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0,
% 12.71/2.53 v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v1) =
% 12.71/2.53 v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0))))
% 12.71/2.53 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 12.71/2.53 (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ~
% 12.71/2.53 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any]
% 12.71/2.53 : ? [v7: any] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2)
% 12.71/2.53 = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~
% 12.71/2.53 (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : !
% 12.71/2.53 [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3)
% 12.71/2.53 | ~ (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 12.71/2.53 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 12.71/2.53 (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 &
% 12.71/2.53 convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v4 =
% 12.71/2.53 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1:
% 12.71/2.53 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) |
% 12.71/2.53 ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 12.71/2.53 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 12.71/2.53 (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 &
% 12.71/2.53 convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 =
% 12.71/2.53 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1:
% 12.71/2.53 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) |
% 12.71/2.53 ~ (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 12.71/2.53 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 12.71/2.53 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v4 &
% 12.71/2.53 convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & ( ~ (v4 =
% 12.71/2.53 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1:
% 12.71/2.53 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~
% 12.71/2.53 (convergent_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 12.71/2.53 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 12.71/2.53 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 &
% 12.71/2.53 convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 =
% 12.71/2.53 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1:
% 12.71/2.53 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~
% 12.71/2.53 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 12.71/2.53 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 12.71/2.53 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 &
% 12.71/2.53 convergent_lines(v1, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v4 =
% 12.71/2.53 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1:
% 12.71/2.53 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) | ~
% 12.71/2.53 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 12.71/2.53 any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 12.71/2.53 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 &
% 12.71/2.53 unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v4
% 12.71/2.53 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : !
% 12.71/2.53 [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) |
% 12.71/2.53 ~ (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 12.71/2.53 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 12.71/2.53 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 &
% 12.71/2.53 unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & ( ~ (v4
% 12.71/2.53 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0))))
% 12.71/2.53
% 12.71/2.54 (ooc1)
% 12.71/2.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (orthogonal_through_point(v1,
% 12.71/2.54 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 12.71/2.54 unorthogonal_lines(v2, v1) = v3))
% 12.71/2.54
% 12.71/2.54 (ooc2)
% 12.71/2.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (orthogonal_through_point(v1,
% 12.71/2.54 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 12.71/2.54 apart_point_and_line(v0, v2) = v3))
% 12.71/2.54
% 12.71/2.54 (ouo1)
% 12.71/2.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 12.71/2.54 int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~
% 12.71/2.54 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ~
% 12.71/2.54 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 12.71/2.54 (unorthogonal_lines(v1, v3) = v7 & apart_point_and_line(v0, v1) = v6 & (v7 =
% 12.71/2.54 0 | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 12.71/2.54 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3)
% 12.71/2.54 = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) |
% 12.71/2.54 ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 12.71/2.54 (unorthogonal_lines(v1, v3) = v8 & apart_point_and_line(v0, v2) = v7 &
% 12.71/2.54 distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0:
% 12.71/2.54 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 12.71/2.54 : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~
% 12.71/2.54 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 12.71/2.54 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 12.71/2.54 (unorthogonal_lines(v2, v3) = v8 & apart_point_and_line(v0, v1) = v7 &
% 12.71/2.54 distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0:
% 12.71/2.54 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 12.71/2.54 : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~
% 12.71/2.54 (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ~
% 12.71/2.54 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 12.71/2.54 (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 =
% 12.71/2.54 0 | v6 = 0)))
% 12.71/2.54
% 12.71/2.54 (function-axioms)
% 12.71/2.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.71/2.55 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 12.71/2.55 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 12.71/2.55 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 12.71/2.55 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 12.71/2.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 12.71/2.55 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 12.71/2.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 12.71/2.55 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 12.71/2.55 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 12.71/2.55 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.71/2.55 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.71/2.55 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 12.71/2.55 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 12.71/2.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 12.71/2.55 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.71/2.55 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.71/2.55 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 12.71/2.55 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.71/2.55 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 12.71/2.55 v0))
% 12.71/2.55
% 12.71/2.55 Further assumptions not needed in the proof:
% 12.71/2.55 --------------------------------------------
% 12.71/2.55 apart1, apart2, apart3, apart4, apart5, apart6, ceq1, ceq2, ceq3, con1, con2,
% 12.71/2.55 cp1, cp2, occu1
% 12.71/2.55
% 12.71/2.55 Those formulas are unsatisfiable:
% 12.71/2.55 ---------------------------------
% 12.71/2.55
% 12.71/2.55 Begin of proof
% 12.71/2.55 |
% 12.71/2.55 | ALPHA: (cu1) implies:
% 12.71/2.55 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 12.71/2.55 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5)
% 12.71/2.55 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3)
% 12.71/2.55 | = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any]
% 12.71/2.55 | : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v3) = v8 &
% 12.71/2.55 | apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 &
% 12.71/2.55 | ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 12.71/2.55 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 12.71/2.55 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5)
% 12.71/2.55 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 12.71/2.55 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ?
% 12.71/2.55 | [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 12.71/2.55 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 12.71/2.55 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0
% 12.71/2.55 | | v8 = 0)))
% 12.71/2.55 |
% 12.71/2.55 | ALPHA: (cup1) implies:
% 12.71/2.55 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.71/2.55 | (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0)
% 12.71/2.55 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 12.71/2.55 | (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 &
% 12.71/2.55 | (v5 = 0 | v4 = 0)))
% 12.71/2.55 |
% 12.71/2.55 | ALPHA: (oac1) implies:
% 12.71/2.56 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 12.71/2.56 | (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0)
% 12.71/2.56 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 12.71/2.56 | ? [v6: any] : ? [v7: any] : (unorthogonal_lines(v1, v2) = v7 &
% 12.71/2.56 | unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 &
% 12.71/2.56 | convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) |
% 12.71/2.56 | (v5 = 0 & v3 = 0))))
% 12.71/2.56 |
% 12.71/2.56 | ALPHA: (ouo1) implies:
% 12.71/2.56 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 12.71/2.56 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) |
% 12.71/2.56 | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 12.71/2.56 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 12.71/2.56 | (unorthogonal_lines(v2, v3) = v8 & apart_point_and_line(v0, v1) = v7
% 12.71/2.56 | & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 12.71/2.56 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 12.71/2.56 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) |
% 12.71/2.56 | ~ (apart_point_and_line(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 12.71/2.56 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 12.71/2.56 | (unorthogonal_lines(v1, v3) = v8 & apart_point_and_line(v0, v2) = v7
% 12.71/2.56 | & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 12.71/2.56 |
% 12.71/2.56 | ALPHA: (function-axioms) implies:
% 12.71/2.56 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.71/2.56 | ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~
% 12.71/2.56 | (distinct_lines(v3, v2) = v0))
% 12.71/2.56 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.71/2.56 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 12.71/2.56 | (apart_point_and_line(v3, v2) = v0))
% 12.71/2.56 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.71/2.56 | ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 12.71/2.56 | (unorthogonal_lines(v3, v2) = v0))
% 12.71/2.56 |
% 12.71/2.56 | DELTA: instantiating (con) with fresh symbols all_23_0, all_23_1, all_23_2,
% 12.71/2.56 | all_23_3, all_23_4, all_23_5 gives:
% 12.71/2.56 | (10) ~ (all_23_1 = 0) & orthogonal_through_point(all_23_3, all_23_4) =
% 12.71/2.56 | all_23_0 & orthogonal_through_point(all_23_3, all_23_5) = all_23_2 &
% 12.71/2.56 | apart_point_and_line(all_23_4, all_23_2) = all_23_1 &
% 12.71/2.56 | distinct_lines(all_23_2, all_23_0) = 0 & $i(all_23_0) & $i(all_23_2) &
% 12.71/2.56 | $i(all_23_3) & $i(all_23_4) & $i(all_23_5)
% 12.71/2.56 |
% 12.71/2.56 | ALPHA: (10) implies:
% 12.71/2.56 | (11) ~ (all_23_1 = 0)
% 12.71/2.56 | (12) $i(all_23_5)
% 12.71/2.56 | (13) $i(all_23_4)
% 12.71/2.56 | (14) $i(all_23_3)
% 12.71/2.56 | (15) $i(all_23_2)
% 12.71/2.56 | (16) $i(all_23_0)
% 12.71/2.57 | (17) distinct_lines(all_23_2, all_23_0) = 0
% 12.71/2.57 | (18) apart_point_and_line(all_23_4, all_23_2) = all_23_1
% 12.71/2.57 | (19) orthogonal_through_point(all_23_3, all_23_5) = all_23_2
% 12.71/2.57 | (20) orthogonal_through_point(all_23_3, all_23_4) = all_23_0
% 12.71/2.57 |
% 12.71/2.57 | GROUND_INST: instantiating (1) with all_23_4, all_23_4, all_23_2, all_23_0,
% 12.71/2.57 | all_23_1, all_23_1, simplifying with (13), (15), (16), (17), (18)
% 12.71/2.57 | gives:
% 12.71/2.57 | (21) all_23_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 12.71/2.57 | (apart_point_and_line(all_23_4, all_23_0) = v2 &
% 12.71/2.57 | apart_point_and_line(all_23_4, all_23_0) = v1 &
% 12.71/2.57 | distinct_points(all_23_4, all_23_4) = v0 & ( ~ (v0 = 0) | v2 = 0 |
% 12.71/2.57 | v1 = 0))
% 12.71/2.57 |
% 12.71/2.57 | GROUND_INST: instantiating (2) with all_23_4, all_23_4, all_23_2, all_23_2,
% 12.71/2.57 | all_23_1, all_23_1, simplifying with (13), (15), (18) gives:
% 12.71/2.57 | (22) all_23_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 12.71/2.57 | any] : (apart_point_and_line(all_23_4, all_23_2) = v3 &
% 12.71/2.57 | apart_point_and_line(all_23_4, all_23_2) = v2 &
% 12.71/2.57 | distinct_lines(all_23_2, all_23_2) = v1 & distinct_points(all_23_4,
% 12.71/2.57 | all_23_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 12.71/2.57 |
% 12.71/2.57 | GROUND_INST: instantiating (3) with all_23_4, all_23_2, all_23_0, all_23_1,
% 12.71/2.57 | simplifying with (13), (15), (16), (17), (18) gives:
% 12.71/2.57 | (23) all_23_1 = 0 | ? [v0: any] : ? [v1: any] :
% 12.71/2.57 | (apart_point_and_line(all_23_4, all_23_0) = v0 &
% 12.71/2.57 | convergent_lines(all_23_2, all_23_0) = v1 & (v1 = 0 | v0 = 0))
% 12.71/2.57 |
% 12.71/2.57 | GROUND_INST: instantiating (ooc1) with all_23_5, all_23_3, all_23_2,
% 12.71/2.57 | simplifying with (12), (14), (19) gives:
% 12.71/2.57 | (24) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_23_2, all_23_3) =
% 12.71/2.57 | v0)
% 12.71/2.57 |
% 12.71/2.57 | GROUND_INST: instantiating (ooc2) with all_23_5, all_23_3, all_23_2,
% 12.71/2.57 | simplifying with (12), (14), (19) gives:
% 12.71/2.57 | (25) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_23_5, all_23_2)
% 12.71/2.57 | = v0)
% 12.71/2.57 |
% 12.71/2.57 | GROUND_INST: instantiating (ooc1) with all_23_4, all_23_3, all_23_0,
% 12.71/2.57 | simplifying with (13), (14), (20) gives:
% 12.71/2.57 | (26) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_23_0, all_23_3) =
% 12.71/2.57 | v0)
% 12.71/2.57 |
% 12.71/2.57 | GROUND_INST: instantiating (ooc2) with all_23_4, all_23_3, all_23_0,
% 12.71/2.57 | simplifying with (13), (14), (20) gives:
% 12.71/2.57 | (27) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_23_4, all_23_0)
% 12.71/2.57 | = v0)
% 12.71/2.57 |
% 12.71/2.57 | DELTA: instantiating (27) with fresh symbol all_30_0 gives:
% 12.71/2.57 | (28) ~ (all_30_0 = 0) & apart_point_and_line(all_23_4, all_23_0) =
% 12.71/2.57 | all_30_0
% 12.71/2.57 |
% 12.71/2.57 | ALPHA: (28) implies:
% 12.71/2.57 | (29) ~ (all_30_0 = 0)
% 12.71/2.57 | (30) apart_point_and_line(all_23_4, all_23_0) = all_30_0
% 12.71/2.57 |
% 12.71/2.57 | DELTA: instantiating (26) with fresh symbol all_32_0 gives:
% 12.71/2.57 | (31) ~ (all_32_0 = 0) & unorthogonal_lines(all_23_0, all_23_3) = all_32_0
% 12.71/2.57 |
% 12.71/2.57 | ALPHA: (31) implies:
% 12.71/2.57 | (32) ~ (all_32_0 = 0)
% 12.71/2.57 | (33) unorthogonal_lines(all_23_0, all_23_3) = all_32_0
% 12.71/2.57 |
% 12.71/2.57 | DELTA: instantiating (25) with fresh symbol all_34_0 gives:
% 12.71/2.58 | (34) ~ (all_34_0 = 0) & apart_point_and_line(all_23_5, all_23_2) =
% 12.71/2.58 | all_34_0
% 12.71/2.58 |
% 12.71/2.58 | ALPHA: (34) implies:
% 12.71/2.58 | (35) ~ (all_34_0 = 0)
% 12.71/2.58 | (36) apart_point_and_line(all_23_5, all_23_2) = all_34_0
% 12.71/2.58 |
% 12.71/2.58 | DELTA: instantiating (24) with fresh symbol all_36_0 gives:
% 12.71/2.58 | (37) ~ (all_36_0 = 0) & unorthogonal_lines(all_23_2, all_23_3) = all_36_0
% 12.71/2.58 |
% 12.71/2.58 | ALPHA: (37) implies:
% 12.71/2.58 | (38) ~ (all_36_0 = 0)
% 12.71/2.58 | (39) unorthogonal_lines(all_23_2, all_23_3) = all_36_0
% 12.71/2.58 |
% 12.71/2.58 | BETA: splitting (23) gives:
% 12.71/2.58 |
% 12.71/2.58 | Case 1:
% 12.71/2.58 | |
% 12.71/2.58 | | (40) all_23_1 = 0
% 12.71/2.58 | |
% 12.71/2.58 | | REDUCE: (11), (40) imply:
% 12.71/2.58 | | (41) $false
% 12.71/2.58 | |
% 12.71/2.58 | | CLOSE: (41) is inconsistent.
% 12.71/2.58 | |
% 12.71/2.58 | Case 2:
% 12.71/2.58 | |
% 12.71/2.58 | | (42) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_23_4,
% 12.71/2.58 | | all_23_0) = v0 & convergent_lines(all_23_2, all_23_0) = v1 & (v1
% 12.71/2.58 | | = 0 | v0 = 0))
% 12.71/2.58 | |
% 12.71/2.58 | | DELTA: instantiating (42) with fresh symbols all_42_0, all_42_1 gives:
% 12.71/2.58 | | (43) apart_point_and_line(all_23_4, all_23_0) = all_42_1 &
% 12.71/2.58 | | convergent_lines(all_23_2, all_23_0) = all_42_0 & (all_42_0 = 0 |
% 12.71/2.58 | | all_42_1 = 0)
% 12.71/2.58 | |
% 12.71/2.58 | | ALPHA: (43) implies:
% 12.71/2.58 | | (44) convergent_lines(all_23_2, all_23_0) = all_42_0
% 12.71/2.58 | | (45) apart_point_and_line(all_23_4, all_23_0) = all_42_1
% 12.71/2.58 | | (46) all_42_0 = 0 | all_42_1 = 0
% 12.71/2.58 | |
% 12.71/2.58 | | BETA: splitting (21) gives:
% 12.71/2.58 | |
% 12.71/2.58 | | Case 1:
% 12.71/2.58 | | |
% 12.71/2.58 | | | (47) all_23_1 = 0
% 12.71/2.58 | | |
% 12.71/2.58 | | | REDUCE: (11), (47) imply:
% 12.71/2.58 | | | (48) $false
% 12.71/2.58 | | |
% 12.71/2.58 | | | CLOSE: (48) is inconsistent.
% 12.71/2.58 | | |
% 12.71/2.58 | | Case 2:
% 12.71/2.58 | | |
% 12.71/2.58 | | | (49) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 12.71/2.58 | | | (apart_point_and_line(all_23_4, all_23_0) = v2 &
% 12.71/2.58 | | | apart_point_and_line(all_23_4, all_23_0) = v1 &
% 12.71/2.58 | | | distinct_points(all_23_4, all_23_4) = v0 & ( ~ (v0 = 0) | v2 = 0
% 12.71/2.58 | | | | v1 = 0))
% 12.71/2.58 | | |
% 12.71/2.58 | | | DELTA: instantiating (49) with fresh symbols all_48_0, all_48_1, all_48_2
% 12.71/2.58 | | | gives:
% 12.71/2.58 | | | (50) apart_point_and_line(all_23_4, all_23_0) = all_48_0 &
% 12.71/2.58 | | | apart_point_and_line(all_23_4, all_23_0) = all_48_1 &
% 12.71/2.58 | | | distinct_points(all_23_4, all_23_4) = all_48_2 & ( ~ (all_48_2 =
% 12.71/2.58 | | | 0) | all_48_0 = 0 | all_48_1 = 0)
% 12.71/2.58 | | |
% 12.71/2.58 | | | ALPHA: (50) implies:
% 12.71/2.58 | | | (51) apart_point_and_line(all_23_4, all_23_0) = all_48_1
% 12.71/2.58 | | | (52) apart_point_and_line(all_23_4, all_23_0) = all_48_0
% 12.71/2.58 | | |
% 12.71/2.58 | | | BETA: splitting (22) gives:
% 12.71/2.58 | | |
% 12.71/2.58 | | | Case 1:
% 12.71/2.58 | | | |
% 12.71/2.58 | | | | (53) all_23_1 = 0
% 12.71/2.58 | | | |
% 12.71/2.58 | | | | REDUCE: (11), (53) imply:
% 12.71/2.58 | | | | (54) $false
% 12.71/2.58 | | | |
% 12.71/2.58 | | | | CLOSE: (54) is inconsistent.
% 12.71/2.58 | | | |
% 12.71/2.58 | | | Case 2:
% 12.71/2.58 | | | |
% 12.71/2.58 | | | | (55) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 12.71/2.58 | | | | (apart_point_and_line(all_23_4, all_23_2) = v3 &
% 12.71/2.58 | | | | apart_point_and_line(all_23_4, all_23_2) = v2 &
% 12.71/2.58 | | | | distinct_lines(all_23_2, all_23_2) = v1 &
% 12.71/2.58 | | | | distinct_points(all_23_4, all_23_4) = v0 & ( ~ (v1 = 0) | ~
% 12.71/2.58 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 12.71/2.58 | | | |
% 12.71/2.58 | | | | DELTA: instantiating (55) with fresh symbols all_58_0, all_58_1,
% 12.71/2.58 | | | | all_58_2, all_58_3 gives:
% 12.71/2.58 | | | | (56) apart_point_and_line(all_23_4, all_23_2) = all_58_0 &
% 12.71/2.58 | | | | apart_point_and_line(all_23_4, all_23_2) = all_58_1 &
% 12.71/2.58 | | | | distinct_lines(all_23_2, all_23_2) = all_58_2 &
% 12.71/2.58 | | | | distinct_points(all_23_4, all_23_4) = all_58_3 & ( ~ (all_58_2 =
% 12.71/2.58 | | | | 0) | ~ (all_58_3 = 0) | all_58_0 = 0 | all_58_1 = 0)
% 12.71/2.58 | | | |
% 12.71/2.58 | | | | ALPHA: (56) implies:
% 12.71/2.58 | | | | (57) apart_point_and_line(all_23_4, all_23_2) = all_58_1
% 12.71/2.58 | | | | (58) apart_point_and_line(all_23_4, all_23_2) = all_58_0
% 12.71/2.58 | | | |
% 12.71/2.58 | | | | GROUND_INST: instantiating (8) with all_23_1, all_58_0, all_23_2,
% 12.71/2.58 | | | | all_23_4, simplifying with (18), (58) gives:
% 12.71/2.58 | | | | (59) all_58_0 = all_23_1
% 12.71/2.58 | | | |
% 12.71/2.59 | | | | GROUND_INST: instantiating (8) with all_58_1, all_58_0, all_23_2,
% 12.71/2.59 | | | | all_23_4, simplifying with (57), (58) gives:
% 12.71/2.59 | | | | (60) all_58_0 = all_58_1
% 12.71/2.59 | | | |
% 12.71/2.59 | | | | GROUND_INST: instantiating (8) with all_48_1, all_48_0, all_23_0,
% 12.71/2.59 | | | | all_23_4, simplifying with (51), (52) gives:
% 12.71/2.59 | | | | (61) all_48_0 = all_48_1
% 12.71/2.59 | | | |
% 12.71/2.59 | | | | GROUND_INST: instantiating (8) with all_42_1, all_48_0, all_23_0,
% 12.71/2.59 | | | | all_23_4, simplifying with (45), (52) gives:
% 12.71/2.59 | | | | (62) all_48_0 = all_42_1
% 12.71/2.59 | | | |
% 12.71/2.59 | | | | GROUND_INST: instantiating (8) with all_30_0, all_48_0, all_23_0,
% 12.71/2.59 | | | | all_23_4, simplifying with (30), (52) gives:
% 12.71/2.59 | | | | (63) all_48_0 = all_30_0
% 12.71/2.59 | | | |
% 12.71/2.59 | | | | COMBINE_EQS: (59), (60) imply:
% 12.71/2.59 | | | | (64) all_58_1 = all_23_1
% 12.71/2.59 | | | |
% 12.71/2.59 | | | | COMBINE_EQS: (61), (62) imply:
% 12.71/2.59 | | | | (65) all_48_1 = all_42_1
% 12.71/2.59 | | | |
% 12.71/2.59 | | | | COMBINE_EQS: (61), (63) imply:
% 12.71/2.59 | | | | (66) all_48_1 = all_30_0
% 12.71/2.59 | | | |
% 12.71/2.59 | | | | COMBINE_EQS: (65), (66) imply:
% 12.71/2.59 | | | | (67) all_42_1 = all_30_0
% 12.71/2.59 | | | |
% 12.71/2.59 | | | | SIMP: (67) implies:
% 12.71/2.59 | | | | (68) all_42_1 = all_30_0
% 12.71/2.59 | | | |
% 12.71/2.59 | | | | BETA: splitting (46) gives:
% 12.71/2.59 | | | |
% 12.71/2.59 | | | | Case 1:
% 12.71/2.59 | | | | |
% 12.71/2.59 | | | | | (69) all_42_0 = 0
% 12.71/2.59 | | | | |
% 12.71/2.59 | | | | | REDUCE: (44), (69) imply:
% 12.71/2.59 | | | | | (70) convergent_lines(all_23_2, all_23_0) = 0
% 12.71/2.59 | | | | |
% 12.71/2.59 | | | | | GROUND_INST: instantiating (2) with all_23_4, all_23_5, all_23_2,
% 12.71/2.59 | | | | | all_23_2, all_23_1, all_34_0, simplifying with (12),
% 12.71/2.59 | | | | | (13), (15), (18), (36) gives:
% 12.71/2.59 | | | | | (71) all_34_0 = 0 | all_23_1 = 0 | ? [v0: any] : ? [v1: any] : ?
% 12.71/2.59 | | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_23_4,
% 12.71/2.59 | | | | | all_23_2) = v2 & apart_point_and_line(all_23_5, all_23_2)
% 12.71/2.59 | | | | | = v3 & distinct_lines(all_23_2, all_23_2) = v1 &
% 12.71/2.59 | | | | | distinct_points(all_23_4, all_23_5) = v0 & ( ~ (v1 = 0) | ~
% 12.71/2.59 | | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 12.71/2.59 | | | | |
% 12.71/2.59 | | | | | GROUND_INST: instantiating (6) with all_23_4, all_23_0, all_23_2,
% 12.71/2.59 | | | | | all_23_3, all_30_0, all_36_0, simplifying with (13),
% 12.71/2.59 | | | | | (14), (15), (16), (30), (39) gives:
% 12.71/2.59 | | | | | (72) all_36_0 = 0 | all_30_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 12.71/2.59 | | | | | [v2: any] : (unorthogonal_lines(all_23_0, all_23_3) = v2 &
% 12.71/2.59 | | | | | apart_point_and_line(all_23_4, all_23_2) = v1 &
% 12.71/2.59 | | | | | distinct_lines(all_23_0, all_23_2) = v0 & ( ~ (v0 = 0) | v2
% 12.71/2.59 | | | | | = 0 | v1 = 0))
% 12.71/2.59 | | | | |
% 12.71/2.59 | | | | | GROUND_INST: instantiating (5) with all_23_4, all_23_2, all_23_0,
% 12.71/2.59 | | | | | all_23_3, all_30_0, all_36_0, simplifying with (13),
% 12.71/2.59 | | | | | (14), (15), (16), (30), (39) gives:
% 12.71/2.59 | | | | | (73) all_36_0 = 0 | all_30_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 12.71/2.59 | | | | | [v2: any] : (unorthogonal_lines(all_23_0, all_23_3) = v2 &
% 12.71/2.59 | | | | | apart_point_and_line(all_23_4, all_23_2) = v1 &
% 12.71/2.59 | | | | | distinct_lines(all_23_2, all_23_0) = v0 & ( ~ (v0 = 0) | v2
% 12.71/2.59 | | | | | = 0 | v1 = 0))
% 12.71/2.59 | | | | |
% 12.71/2.59 | | | | | GROUND_INST: instantiating (4) with all_23_2, all_23_0, all_23_3,
% 12.71/2.59 | | | | | all_36_0, simplifying with (14), (15), (16), (39), (70)
% 12.71/2.59 | | | | | gives:
% 12.71/2.59 | | | | | (74) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 12.71/2.59 | | | | | (unorthogonal_lines(all_23_0, all_23_3) = v3 &
% 12.71/2.59 | | | | | unorthogonal_lines(all_23_2, all_23_0) = v0 &
% 12.71/2.59 | | | | | convergent_lines(all_23_0, all_23_3) = v2 &
% 12.71/2.59 | | | | | convergent_lines(all_23_2, all_23_3) = v1 & ( ~ (v0 = 0) |
% 12.71/2.59 | | | | | (v3 = 0 & v2 = 0) | (v1 = 0 & all_36_0 = 0)))
% 12.71/2.59 | | | | |
% 12.71/2.59 | | | | | DELTA: instantiating (74) with fresh symbols all_83_0, all_83_1,
% 12.71/2.59 | | | | | all_83_2, all_83_3 gives:
% 12.71/2.59 | | | | | (75) unorthogonal_lines(all_23_0, all_23_3) = all_83_0 &
% 12.71/2.59 | | | | | unorthogonal_lines(all_23_2, all_23_0) = all_83_3 &
% 12.71/2.59 | | | | | convergent_lines(all_23_0, all_23_3) = all_83_1 &
% 12.71/2.59 | | | | | convergent_lines(all_23_2, all_23_3) = all_83_2 & ( ~
% 12.71/2.59 | | | | | (all_83_3 = 0) | (all_83_0 = 0 & all_83_1 = 0) | (all_83_2 =
% 12.71/2.59 | | | | | 0 & all_36_0 = 0))
% 12.71/2.59 | | | | |
% 12.71/2.59 | | | | | ALPHA: (75) implies:
% 12.71/2.59 | | | | | (76) unorthogonal_lines(all_23_0, all_23_3) = all_83_0
% 12.71/2.59 | | | | |
% 12.71/2.59 | | | | | BETA: splitting (71) gives:
% 12.71/2.59 | | | | |
% 12.71/2.59 | | | | | Case 1:
% 12.71/2.59 | | | | | |
% 12.71/2.59 | | | | | | (77) all_34_0 = 0
% 12.71/2.59 | | | | | |
% 12.71/2.59 | | | | | | REDUCE: (35), (77) imply:
% 12.71/2.59 | | | | | | (78) $false
% 12.71/2.59 | | | | | |
% 12.71/2.59 | | | | | | CLOSE: (78) is inconsistent.
% 12.71/2.59 | | | | | |
% 12.71/2.59 | | | | | Case 2:
% 12.71/2.59 | | | | | |
% 12.71/2.59 | | | | | | (79) all_23_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 12.71/2.59 | | | | | | ? [v3: any] : (apart_point_and_line(all_23_4, all_23_2) = v2
% 12.71/2.59 | | | | | | & apart_point_and_line(all_23_5, all_23_2) = v3 &
% 12.71/2.59 | | | | | | distinct_lines(all_23_2, all_23_2) = v1 &
% 12.71/2.59 | | | | | | distinct_points(all_23_4, all_23_5) = v0 & ( ~ (v1 = 0) |
% 12.71/2.59 | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 12.71/2.59 | | | | | |
% 12.71/2.59 | | | | | | BETA: splitting (73) gives:
% 12.71/2.59 | | | | | |
% 12.71/2.59 | | | | | | Case 1:
% 12.71/2.59 | | | | | | |
% 12.71/2.59 | | | | | | | (80) all_36_0 = 0
% 12.71/2.59 | | | | | | |
% 12.71/2.59 | | | | | | | REDUCE: (38), (80) imply:
% 12.71/2.59 | | | | | | | (81) $false
% 12.71/2.59 | | | | | | |
% 12.71/2.59 | | | | | | | CLOSE: (81) is inconsistent.
% 12.71/2.59 | | | | | | |
% 12.71/2.59 | | | | | | Case 2:
% 12.71/2.59 | | | | | | |
% 12.71/2.60 | | | | | | | (82) all_30_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any]
% 12.71/2.60 | | | | | | | : (unorthogonal_lines(all_23_0, all_23_3) = v2 &
% 12.71/2.60 | | | | | | | apart_point_and_line(all_23_4, all_23_2) = v1 &
% 12.71/2.60 | | | | | | | distinct_lines(all_23_2, all_23_0) = v0 & ( ~ (v0 = 0) |
% 12.71/2.60 | | | | | | | v2 = 0 | v1 = 0))
% 12.71/2.60 | | | | | | |
% 12.71/2.60 | | | | | | | BETA: splitting (82) gives:
% 12.71/2.60 | | | | | | |
% 12.71/2.60 | | | | | | | Case 1:
% 12.71/2.60 | | | | | | | |
% 12.71/2.60 | | | | | | | | (83) all_30_0 = 0
% 12.71/2.60 | | | | | | | |
% 12.71/2.60 | | | | | | | | REDUCE: (29), (83) imply:
% 12.71/2.60 | | | | | | | | (84) $false
% 12.71/2.60 | | | | | | | |
% 12.71/2.60 | | | | | | | | CLOSE: (84) is inconsistent.
% 12.71/2.60 | | | | | | | |
% 12.71/2.60 | | | | | | | Case 2:
% 12.71/2.60 | | | | | | | |
% 12.71/2.60 | | | | | | | | (85) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 12.71/2.60 | | | | | | | | (unorthogonal_lines(all_23_0, all_23_3) = v2 &
% 12.71/2.60 | | | | | | | | apart_point_and_line(all_23_4, all_23_2) = v1 &
% 12.71/2.60 | | | | | | | | distinct_lines(all_23_2, all_23_0) = v0 & ( ~ (v0 = 0)
% 12.71/2.60 | | | | | | | | | v2 = 0 | v1 = 0))
% 12.71/2.60 | | | | | | | |
% 12.71/2.60 | | | | | | | | DELTA: instantiating (85) with fresh symbols all_141_0,
% 12.71/2.60 | | | | | | | | all_141_1, all_141_2 gives:
% 12.71/2.60 | | | | | | | | (86) unorthogonal_lines(all_23_0, all_23_3) = all_141_0 &
% 12.71/2.60 | | | | | | | | apart_point_and_line(all_23_4, all_23_2) = all_141_1 &
% 12.71/2.60 | | | | | | | | distinct_lines(all_23_2, all_23_0) = all_141_2 & ( ~
% 12.71/2.60 | | | | | | | | (all_141_2 = 0) | all_141_0 = 0 | all_141_1 = 0)
% 12.71/2.60 | | | | | | | |
% 12.71/2.60 | | | | | | | | ALPHA: (86) implies:
% 12.71/2.60 | | | | | | | | (87) distinct_lines(all_23_2, all_23_0) = all_141_2
% 12.71/2.60 | | | | | | | | (88) apart_point_and_line(all_23_4, all_23_2) = all_141_1
% 12.71/2.60 | | | | | | | | (89) unorthogonal_lines(all_23_0, all_23_3) = all_141_0
% 12.71/2.60 | | | | | | | | (90) ~ (all_141_2 = 0) | all_141_0 = 0 | all_141_1 = 0
% 12.71/2.60 | | | | | | | |
% 12.71/2.60 | | | | | | | | BETA: splitting (72) gives:
% 12.71/2.60 | | | | | | | |
% 12.71/2.60 | | | | | | | | Case 1:
% 12.71/2.60 | | | | | | | | |
% 12.71/2.60 | | | | | | | | | (91) all_36_0 = 0
% 12.71/2.60 | | | | | | | | |
% 12.71/2.60 | | | | | | | | | REDUCE: (38), (91) imply:
% 12.71/2.60 | | | | | | | | | (92) $false
% 12.71/2.60 | | | | | | | | |
% 12.71/2.60 | | | | | | | | | CLOSE: (92) is inconsistent.
% 12.71/2.60 | | | | | | | | |
% 12.71/2.60 | | | | | | | | Case 2:
% 12.71/2.60 | | | | | | | | |
% 12.71/2.60 | | | | | | | | | (93) all_30_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 12.71/2.60 | | | | | | | | | any] : (unorthogonal_lines(all_23_0, all_23_3) = v2
% 12.71/2.60 | | | | | | | | | & apart_point_and_line(all_23_4, all_23_2) = v1 &
% 12.71/2.60 | | | | | | | | | distinct_lines(all_23_0, all_23_2) = v0 & ( ~ (v0 =
% 12.71/2.60 | | | | | | | | | 0) | v2 = 0 | v1 = 0))
% 12.71/2.60 | | | | | | | | |
% 12.71/2.60 | | | | | | | | | BETA: splitting (79) gives:
% 12.71/2.60 | | | | | | | | |
% 12.71/2.60 | | | | | | | | | Case 1:
% 12.71/2.60 | | | | | | | | | |
% 12.71/2.60 | | | | | | | | | | (94) all_23_1 = 0
% 12.71/2.60 | | | | | | | | | |
% 12.71/2.60 | | | | | | | | | | REDUCE: (11), (94) imply:
% 12.71/2.60 | | | | | | | | | | (95) $false
% 12.71/2.60 | | | | | | | | | |
% 12.71/2.60 | | | | | | | | | | CLOSE: (95) is inconsistent.
% 12.71/2.60 | | | | | | | | | |
% 12.71/2.60 | | | | | | | | | Case 2:
% 12.71/2.60 | | | | | | | | | |
% 12.71/2.60 | | | | | | | | | | (96) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 12.71/2.60 | | | | | | | | | | any] : (apart_point_and_line(all_23_4, all_23_2) =
% 12.71/2.60 | | | | | | | | | | v2 & apart_point_and_line(all_23_5, all_23_2) = v3
% 12.71/2.60 | | | | | | | | | | & distinct_lines(all_23_2, all_23_2) = v1 &
% 12.71/2.60 | | | | | | | | | | distinct_points(all_23_4, all_23_5) = v0 & ( ~ (v1
% 12.71/2.60 | | | | | | | | | | = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 12.71/2.60 | | | | | | | | | |
% 12.71/2.60 | | | | | | | | | | DELTA: instantiating (96) with fresh symbols all_179_0,
% 12.71/2.60 | | | | | | | | | | all_179_1, all_179_2, all_179_3 gives:
% 12.71/2.60 | | | | | | | | | | (97) apart_point_and_line(all_23_4, all_23_2) = all_179_1
% 12.71/2.60 | | | | | | | | | | & apart_point_and_line(all_23_5, all_23_2) =
% 12.71/2.60 | | | | | | | | | | all_179_0 & distinct_lines(all_23_2, all_23_2) =
% 12.71/2.60 | | | | | | | | | | all_179_2 & distinct_points(all_23_4, all_23_5) =
% 12.71/2.60 | | | | | | | | | | all_179_3 & ( ~ (all_179_2 = 0) | ~ (all_179_3 = 0)
% 12.71/2.60 | | | | | | | | | | | all_179_0 = 0 | all_179_1 = 0)
% 12.71/2.60 | | | | | | | | | |
% 12.71/2.60 | | | | | | | | | | ALPHA: (97) implies:
% 12.71/2.60 | | | | | | | | | | (98) apart_point_and_line(all_23_4, all_23_2) = all_179_1
% 12.71/2.60 | | | | | | | | | |
% 12.71/2.60 | | | | | | | | | | BETA: splitting (93) gives:
% 12.71/2.60 | | | | | | | | | |
% 12.71/2.60 | | | | | | | | | | Case 1:
% 12.71/2.60 | | | | | | | | | | |
% 12.71/2.60 | | | | | | | | | | | (99) all_30_0 = 0
% 12.71/2.60 | | | | | | | | | | |
% 12.71/2.60 | | | | | | | | | | | REDUCE: (29), (99) imply:
% 12.71/2.60 | | | | | | | | | | | (100) $false
% 12.71/2.60 | | | | | | | | | | |
% 12.71/2.60 | | | | | | | | | | | CLOSE: (100) is inconsistent.
% 12.71/2.60 | | | | | | | | | | |
% 12.71/2.60 | | | | | | | | | | Case 2:
% 12.71/2.60 | | | | | | | | | | |
% 12.71/2.60 | | | | | | | | | | | (101) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 12.71/2.60 | | | | | | | | | | | (unorthogonal_lines(all_23_0, all_23_3) = v2 &
% 12.71/2.60 | | | | | | | | | | | apart_point_and_line(all_23_4, all_23_2) = v1 &
% 12.71/2.60 | | | | | | | | | | | distinct_lines(all_23_0, all_23_2) = v0 & ( ~
% 12.71/2.60 | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0))
% 12.71/2.60 | | | | | | | | | | |
% 12.71/2.60 | | | | | | | | | | | DELTA: instantiating (101) with fresh symbols all_189_0,
% 12.71/2.60 | | | | | | | | | | | all_189_1, all_189_2 gives:
% 12.71/2.60 | | | | | | | | | | | (102) unorthogonal_lines(all_23_0, all_23_3) = all_189_0
% 12.71/2.60 | | | | | | | | | | | & apart_point_and_line(all_23_4, all_23_2) =
% 12.71/2.60 | | | | | | | | | | | all_189_1 & distinct_lines(all_23_0, all_23_2) =
% 12.71/2.60 | | | | | | | | | | | all_189_2 & ( ~ (all_189_2 = 0) | all_189_0 = 0 |
% 12.71/2.60 | | | | | | | | | | | all_189_1 = 0)
% 12.71/2.60 | | | | | | | | | | |
% 12.71/2.60 | | | | | | | | | | | ALPHA: (102) implies:
% 12.71/2.60 | | | | | | | | | | | (103) apart_point_and_line(all_23_4, all_23_2) =
% 12.71/2.60 | | | | | | | | | | | all_189_1
% 12.71/2.60 | | | | | | | | | | | (104) unorthogonal_lines(all_23_0, all_23_3) = all_189_0
% 12.71/2.60 | | | | | | | | | | |
% 13.22/2.60 | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_141_2, all_23_0,
% 13.22/2.60 | | | | | | | | | | | all_23_2, simplifying with (17), (87) gives:
% 13.22/2.60 | | | | | | | | | | | (105) all_141_2 = 0
% 13.22/2.60 | | | | | | | | | | |
% 13.22/2.60 | | | | | | | | | | | GROUND_INST: instantiating (8) with all_141_1, all_179_1,
% 13.22/2.60 | | | | | | | | | | | all_23_2, all_23_4, simplifying with (88), (98)
% 13.22/2.60 | | | | | | | | | | | gives:
% 13.22/2.60 | | | | | | | | | | | (106) all_179_1 = all_141_1
% 13.22/2.60 | | | | | | | | | | |
% 13.22/2.60 | | | | | | | | | | | GROUND_INST: instantiating (8) with all_23_1, all_189_1,
% 13.22/2.60 | | | | | | | | | | | all_23_2, all_23_4, simplifying with (18), (103)
% 13.22/2.60 | | | | | | | | | | | gives:
% 13.22/2.60 | | | | | | | | | | | (107) all_189_1 = all_23_1
% 13.22/2.60 | | | | | | | | | | |
% 13.22/2.60 | | | | | | | | | | | GROUND_INST: instantiating (8) with all_179_1, all_189_1,
% 13.22/2.60 | | | | | | | | | | | all_23_2, all_23_4, simplifying with (98), (103)
% 13.22/2.60 | | | | | | | | | | | gives:
% 13.22/2.60 | | | | | | | | | | | (108) all_189_1 = all_179_1
% 13.22/2.60 | | | | | | | | | | |
% 13.22/2.60 | | | | | | | | | | | GROUND_INST: instantiating (9) with all_32_0, all_141_0,
% 13.22/2.60 | | | | | | | | | | | all_23_3, all_23_0, simplifying with (33), (89)
% 13.22/2.60 | | | | | | | | | | | gives:
% 13.22/2.60 | | | | | | | | | | | (109) all_141_0 = all_32_0
% 13.22/2.60 | | | | | | | | | | |
% 13.22/2.60 | | | | | | | | | | | GROUND_INST: instantiating (9) with all_141_0, all_189_0,
% 13.22/2.60 | | | | | | | | | | | all_23_3, all_23_0, simplifying with (89), (104)
% 13.22/2.60 | | | | | | | | | | | gives:
% 13.22/2.60 | | | | | | | | | | | (110) all_189_0 = all_141_0
% 13.22/2.60 | | | | | | | | | | |
% 13.22/2.60 | | | | | | | | | | | GROUND_INST: instantiating (9) with all_83_0, all_189_0,
% 13.22/2.60 | | | | | | | | | | | all_23_3, all_23_0, simplifying with (76), (104)
% 13.22/2.60 | | | | | | | | | | | gives:
% 13.22/2.61 | | | | | | | | | | | (111) all_189_0 = all_83_0
% 13.22/2.61 | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | COMBINE_EQS: (110), (111) imply:
% 13.22/2.61 | | | | | | | | | | | (112) all_141_0 = all_83_0
% 13.22/2.61 | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | SIMP: (112) implies:
% 13.22/2.61 | | | | | | | | | | | (113) all_141_0 = all_83_0
% 13.22/2.61 | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | COMBINE_EQS: (107), (108) imply:
% 13.22/2.61 | | | | | | | | | | | (114) all_179_1 = all_23_1
% 13.22/2.61 | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | SIMP: (114) implies:
% 13.22/2.61 | | | | | | | | | | | (115) all_179_1 = all_23_1
% 13.22/2.61 | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | COMBINE_EQS: (106), (115) imply:
% 13.22/2.61 | | | | | | | | | | | (116) all_141_1 = all_23_1
% 13.22/2.61 | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | SIMP: (116) implies:
% 13.22/2.61 | | | | | | | | | | | (117) all_141_1 = all_23_1
% 13.22/2.61 | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | COMBINE_EQS: (109), (113) imply:
% 13.22/2.61 | | | | | | | | | | | (118) all_83_0 = all_32_0
% 13.22/2.61 | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | BETA: splitting (90) gives:
% 13.22/2.61 | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | Case 1:
% 13.22/2.61 | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | | (119) ~ (all_141_2 = 0)
% 13.22/2.61 | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | | REDUCE: (105), (119) imply:
% 13.22/2.61 | | | | | | | | | | | | (120) $false
% 13.22/2.61 | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | | CLOSE: (120) is inconsistent.
% 13.22/2.61 | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | Case 2:
% 13.22/2.61 | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | | (121) all_141_0 = 0 | all_141_1 = 0
% 13.22/2.61 | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | | BETA: splitting (121) gives:
% 13.22/2.61 | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | | Case 1:
% 13.22/2.61 | | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | | | (122) all_141_0 = 0
% 13.22/2.61 | | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | | | COMBINE_EQS: (109), (122) imply:
% 13.22/2.61 | | | | | | | | | | | | | (123) all_32_0 = 0
% 13.22/2.61 | | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | | | REDUCE: (32), (123) imply:
% 13.22/2.61 | | | | | | | | | | | | | (124) $false
% 13.22/2.61 | | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | | | CLOSE: (124) is inconsistent.
% 13.22/2.61 | | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | | Case 2:
% 13.22/2.61 | | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | | | (125) all_141_1 = 0
% 13.22/2.61 | | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | | | COMBINE_EQS: (117), (125) imply:
% 13.22/2.61 | | | | | | | | | | | | | (126) all_23_1 = 0
% 13.22/2.61 | | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | | | REDUCE: (11), (126) imply:
% 13.22/2.61 | | | | | | | | | | | | | (127) $false
% 13.22/2.61 | | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | | | CLOSE: (127) is inconsistent.
% 13.22/2.61 | | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | | End of split
% 13.22/2.61 | | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | | End of split
% 13.22/2.61 | | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | | End of split
% 13.22/2.61 | | | | | | | | | |
% 13.22/2.61 | | | | | | | | | End of split
% 13.22/2.61 | | | | | | | | |
% 13.22/2.61 | | | | | | | | End of split
% 13.22/2.61 | | | | | | | |
% 13.22/2.61 | | | | | | | End of split
% 13.22/2.61 | | | | | | |
% 13.22/2.61 | | | | | | End of split
% 13.22/2.61 | | | | | |
% 13.22/2.61 | | | | | End of split
% 13.22/2.61 | | | | |
% 13.22/2.61 | | | | Case 2:
% 13.22/2.61 | | | | |
% 13.22/2.61 | | | | | (128) all_42_1 = 0
% 13.22/2.61 | | | | |
% 13.22/2.61 | | | | | COMBINE_EQS: (68), (128) imply:
% 13.22/2.61 | | | | | (129) all_30_0 = 0
% 13.22/2.61 | | | | |
% 13.22/2.61 | | | | | SIMP: (129) implies:
% 13.22/2.61 | | | | | (130) all_30_0 = 0
% 13.22/2.61 | | | | |
% 13.22/2.61 | | | | | REDUCE: (29), (130) imply:
% 13.22/2.61 | | | | | (131) $false
% 13.22/2.61 | | | | |
% 13.22/2.61 | | | | | CLOSE: (131) is inconsistent.
% 13.22/2.61 | | | | |
% 13.22/2.61 | | | | End of split
% 13.22/2.61 | | | |
% 13.22/2.61 | | | End of split
% 13.22/2.61 | | |
% 13.22/2.61 | | End of split
% 13.22/2.61 | |
% 13.22/2.61 | End of split
% 13.22/2.61 |
% 13.22/2.61 End of proof
% 13.22/2.61 % SZS output end Proof for theBenchmark
% 13.22/2.61
% 13.22/2.61 1995ms
%------------------------------------------------------------------------------